{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Solutions from a student (dragged) 32

Solutions from a student (dragged) 32 - Part(c To get two...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Part (b): We now want to count the number of n -digit numbers where the digit 0 appears i times. Lets pick the locations where we want to place the zeros. This can be done in n i ways. We then have nine choices for the other digits to place in the other n - i locations. This gives 9 n - i possible enoumerations for non-zero digits. In total then we have n i 9 n - i , n digit numbers with i zeros in them. Problem 9 (selecting three students from three classes) Part (a): To choose three students from 3 n total students can be done in 3 n 3 ways. Part (b): To pick three students from the same class we must first pick the class to draw the student from. This can be done in 3 1 = 3 ways. Once the class has been picked we have to pick the three students in from the n in that class. This can be done in n 3 ways. Thus in total we have 3 n 3 , possible selections of three students all from one class.
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Part (c): To get two students in the same class and another in a di±erent class, we must Frst pick the class from which to draw the two students from. This can be done in ± 3 1 ² = 3 ways. Next we pick the other class from which to draw the singleton student from. Since there are two possible classes to select this student from this can be done in two ways. Once both of these classes are selected we pick the individual two and one students from their respective classes in ± n 2 ² and ± n 1 ² ways respectively. Thus in total we have 3 · 2 · ± n 2 ²± n 1 ² = 6 n n ( n-1) 2 = 3 n 2 ( n-1) , ways. Part (d): Three students (all from a di±erent class) can be picked in ± n 1 ² 3 = n 3 ways. Part (e): As an identity we have then that ± 3 n 3 ² = 3 ± n 3 ² + 3 n 2 ( n-1) + n 3 ....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern